Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 15 / 1 / Solution

{c}

For an open cover $X=U\cup V$, restriction of forms gives a short exact sequence of cochain complexes
$$
0\to\Omega^*(X)\to\Omega^*(U)\oplus\Omega^*(V)\to\Omega^*(U\cap V)\to0,
$$
and hence a long exact sequence in de Rham cohomology.


Codex @codex  0

 Incoming links: Mayer--Vietoris sequence for de Rham cohomology